Properties

Label 16.6.a
Level $16$
Weight $6$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $12$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(16))\).

Total New Old
Modular forms 13 3 10
Cusp forms 7 2 5
Eisenstein series 6 1 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2 q - 8 q^{3} - 20 q^{5} + 112 q^{7} + 58 q^{9} + O(q^{10}) \) \( 2 q - 8 q^{3} - 20 q^{5} + 112 q^{7} + 58 q^{9} - 664 q^{11} + 60 q^{13} + 2128 q^{15} - 604 q^{17} - 3880 q^{19} + 576 q^{21} + 3920 q^{23} + 2142 q^{25} - 2384 q^{27} - 3876 q^{29} + 1472 q^{31} - 4000 q^{33} + 2976 q^{35} + 10028 q^{37} - 14576 q^{39} + 8340 q^{41} + 21288 q^{43} - 16964 q^{45} - 22368 q^{47} - 25294 q^{49} + 31088 q^{51} + 31180 q^{53} - 19984 q^{55} + 50848 q^{57} - 9208 q^{59} - 53220 q^{61} - 4944 q^{63} - 57944 q^{65} - 6280 q^{67} + 52928 q^{69} + 78832 q^{71} + 62676 q^{73} - 49528 q^{75} - 50496 q^{77} + 32352 q^{79} - 97742 q^{81} - 135080 q^{83} + 120728 q^{85} + 58512 q^{87} + 101748 q^{89} - 25312 q^{91} - 165632 q^{93} + 180112 q^{95} - 73532 q^{97} + 33992 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
16.6.a.a 16.a 1.a $1$ $2.566$ \(\Q\) None \(0\) \(-20\) \(-74\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b 16.a 1.a $1$ $2.566$ \(\Q\) None \(0\) \(12\) \(54\) \(88\) $-$ $\mathrm{SU}(2)$ \(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)